Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int main() {
  ios_base::sync_with_stdio(0);
  vector<int> a;
  for (long long i = 1; i * (i + 1) / 2 <= 1000000000; ++i)
    a.push_back(i * (i + 1) / 2);
  int n;
  while (cin >> n) {
    string res = "NO";
    for (int i = 0; i < a.size() && a[i] < n; ++i) {
      int k = n - a[i];
      if (*lower_bound((a).begin(), (a).end(), k) == k) {
        res = "YES";
        break;
      }
    }
    cout << res << endl;
  }
  return 0;
}